Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 0.5n(n − 1) + 1, for almost a...
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| Дата: | 2010 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146096 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups / E. García-Río // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1460962019-02-08T01:23:33Z Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups Calvaruso, G. García-Río, E. Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 0.5n(n − 1) + 1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvature tensor of these spaces satisfi several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov–Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and P-spaces, and that ε-spaces are Ivanov–Petrova and curvature-curvature commuting manifolds. 2010 Article Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups / E. García-Río // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C50; 53C20 http://dspace.nbuv.gov.ua/handle/123456789/146096 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Together with spaces of constant sectional curvature and products of a real line
with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 0.5n(n − 1) + 1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvature tensor of these spaces satisfi several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov–Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and P-spaces, and that ε-spaces are Ivanov–Petrova and curvature-curvature commuting manifolds. |
| format |
Article |
| author |
Calvaruso, G. García-Río, E. |
| spellingShingle |
Calvaruso, G. García-Río, E. Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Calvaruso, G. García-Río, E. |
| author_sort |
Calvaruso, G. |
| title |
Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_short |
Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_full |
Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_fullStr |
Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_full_unstemmed |
Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_sort |
algebraic properties of curvature operators in lorentzian manifolds with large isometry groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146096 |
| citation_txt |
Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups / E. García-Río // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT calvarusog algebraicpropertiesofcurvatureoperatorsinlorentzianmanifoldswithlargeisometrygroups AT garciarioe algebraicpropertiesofcurvatureoperatorsinlorentzianmanifoldswithlargeisometrygroups |
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2023-05-20T17:23:48Z |
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2023-05-20T17:23:48Z |
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